The best, time-tested way to secretly open a sealed envelope is to use steam to dissolve the glue that seals the paper. So set a kettle full of water to boil on the stove.
Once the kettle begins to steam, stick the handle of a spoon in the spout to keep a steady stream of steam coming out of the kettle.
Find an oven glove or some other way to protect your hand from getting burned. Once protected, hold the back side (the glued side) of the envelope in the path of the steam.
Leave the envelope in the steam for about 15 seconds at a time so that the steam does not completely drench the paper. After the first 15 seconds, remove the envelope from the steam and place it on a flat surface.
Use a thin blade knife or letter opener to very gently pry the flap of the envelope from the back. The seal should break on its own, so do not try to force it or it will tear. If the flap does not lift off the envelope back, give it another steam treatment. If the flap does lift off, then you are free to read the envelope's contents without anyone else knowing.
Reseal the envelope with a thin strip of rubber cement or a glue stick. Either way, go light on the glue. There is no better tip-off that an envelope has been tampered with than a careless smear of glue on the back side.